Integration operators between Bloch type spaces and growth spaces on the unit ball of a complex Banach space

2021 ◽  
Author(s):  
Jiale Chen ◽  
Maofa Wang
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Complex Banach Space ◽  
Type Spaces

scholarly journals Complex extreme measurable selections

1995 ◽  
Vol 58 (2) ◽  
pp. 222-231
Author(s):  
Douglas Mupasiri
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Point ◽  
Measure Space ◽  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Closed Unit Ball ◽  
Measurable Selections ◽  
Necessary And Sufficient

AbstractWe give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.

scholarly journals Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Jianfei Wang
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Arbitrary Order ◽  
Complex Banach Space ◽  
Holomorphic Mappings ◽  
Partial Derivatives ◽  
Carathéodory Metric ◽  
Homogeneous Ball ◽  
Derivatives Of

LetBXbe the unit ball in a complex Banach spaceX. AssumeBXis homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ballBntoBXassociated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.

scholarly journals On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qing-Hua Xu ◽  
Tai-Shun Liu
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Unit Disk ◽  
Univalent Functions ◽  
Complex Banach Space ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Unit Polydisk ◽  
Starlike Mappings

LetSbe the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known resultmaxf∈S⁡a3-λa22=1+2e-2λ/(1-λ)forλ∈0, 1. We investigate the corresponding problem for the class of starlike mappings defined on the unit ball in a complex Banach space or on the unit polydisk inCn, which satisfies a certain condition.

scholarly journals Essential Norm of Operators into Weighted-Type Spaces on the Unit Ball

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Pablo Galindo ◽  
Mikael Lindström ◽  
Stevo Stević
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Type Space ◽  
Type Spaces ◽  
Weighted Type ◽  
General Banach Space

The essential norm of any operator from a general Banach space of holomorphic functions on the unit ball inℂninto the little weighted-type space is calculated. Some applications of the formula are given.

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